Split eight litres in half with a 5 and a 3

Question

You have three unmarked jugs of 8, 5 and 3 litres. The 8-litre jug is full of water; the other two are empty. There is no tap and no drain: the only thing you can do is pour from one jug into another until the source is empty or the target is full. Divide the water into two equal shares of 4 litres each. What is the smallest number of pours that does it?

Accepted Answer

Seven pours. Write the state as (8-jug, 5-jug, 3-jug). 1. Pour 8 into 5: (3, 5, 0) 2. Pour 5 into 3: (3, 2, 3) 3. Pour 3 into 8: (6, 2, 0) 4. Pour 5 into 3: (6, 0, 2) 5. Pour 8 into 5: (1, 5, 2) 6. Pour 5 into 3; only 1 litre fits: (1, 4, 3) 7. Pour 3 into 8: (4, 4, 0) Four litres in the big jug and four in the middle jug. Why it needs seven. With no tap, the total is fixed at 8 and the only moves are pours, so the number of reachable states is small (fewer than twenty). Checking them level by level shows that (4, 4, 0) first appears at depth seven. A different seven-pour route exists that st…

Split eight litres in half with a 5 and a 3

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